Electric filter

A transmission network used to selectively modify the
components of a signal according to their frequencies. In most cases
a filter is used to enhance signals of desired frequencies while suppressing
signals of undesired frequencies. An ideal filter would pass only desired
frequencies while completely suppressing all unwanted frequencies, without
any dispersion in time of the frequencies. Unfortunately, ideal filters
are impossible to achieve.

Electric filters are used in most electronic communication systems.
Whether communication is over wire, free space, or optical fiber, multiple
channels of information can be multiplexed on different frequency bands.
Unwanted signals and noise are introduced along the communications path.
The main function of electric filters is to separate the desired signal
or channel from all others and from any noise or interference. For example,
an AM radio receiver may have a low-pass filter after the antenna to
separate the AM frequency band from higher frequency bands and , elsewhere
in the radio, a band-pass filter to select the desired station out of
the AM band.

Although electronic filters are commonly thought of as devices for
conferring selectivity to communication paths, they are used in almost
every part of electronic equipment, such as the damping element in phase-locked
loops, cleanup devices for frequency sources, and pulse expansion and compression devices for radar. One of the simplest and most common filters
is the bypass capacitor used to restrict high-frequency electronic noise.

Filters are characterized in multiple ways. The expression low-pass,
Butterworth, LC describes a filter. The descriptior low-pass indicates
the relation of the passed to the rejected frequencies. Butterworth describes
the type of polynomials in the transfer function. LC indicates the construction
method. This filter is made of inductors (L's) and capacitors (C's).

Filters are classified by the relationship of the frequencies that
are selectively passed, referred to as the passband, to those which are
attenuated, referred to as the stopband. An ideal low-pass filter passes
all frequencies below a specified cutoff frequency and rejects those
above. A high-pass filter does the opposite. An ideal band-pass filter
will pass a band of frequencies while rejecting all others; a band-reject
filter will reject a band of frequencies and pass all others.

An all-pass filter passes all frequencies but does, however, modify
the time delay characteristics. It normally corrects delay distortions
caused by other sections of a communication path.

All the above classifications are based on frequency-domain considerations.
In addition, there are two terms that apply to the time-response characteristics
of a filter. A finite impulse response (FIR) filter, when exposed to
a change in input, will settle to a steady state within a finite amount
of time. An infinite impulse response (IIR) filter will continue oscillating
in a decaying manner forever.

A further consideration in classifying a filter is whether the frequency
response is constant in time or varies. If it varies with time, as a
function of the input signal, it's known as an adaptive filter. This
type of filter finds use in speech and image enhancement and echo cancellation.

Because filters are used over wide frequency and bandwidth ranges and with such varying performance criteria, many methods have been devised
for creating a filter function..

Acoustic filters include crystal, ceramic, mechanical, and surface-acoustic-wave
(SAW) filters. These devices convert electrical energy to mechanical
vibrations, process the signal acoustically, and then convert the energy
back to an electrical form. The equations describing a mechanically vibrating
resonator, where energy is cycled between kinetic motion and stress,
match those of an inductor and capacitor (LC) attached in parallel, where
energy is cycled between the electric field of the capacitor and the
magnetic field of the inductor. However, the mechanical resonators have
much higher Q's and better stability than the LC circuit. With the addition
of a transducer to convert electrical energy to acoustic, the LC circuits
can be replaced with mechanical resonators.

Many techniques are used to create filters. Inductors are re placed
with transistor networks in active filters, discussed below, to reduce
size and cost. By using an analog-to-digital converter the transfer function
can be created mathematically by a digital processor. At high frequencies,
transmission lines and waveguide structures replace lumped elements.

An active filter comprises resistors, capacitors, and active elements
such as operational amplifiers. It's also referred to as an active-RC
filter.

Active filters can realize the same filter characteristics as passive
ones comprising resistor, capacitor, and inductor elements. They have,
however, several advantages over their passive counterparts:

1. Active filters can provide gain, and are frequently used to simultaneously
match filtering (frequency-determining) and gain specifications.

2. They are readily implemented in integrated-circuit technology, whereas
the inductor element of passive filters is not readily realized. As a
result, the active filter is inexpensive, and is attractive for its small
size and weight. In addition, it's readily included with other signal-processing
functions on a single integrated circuit.

3. The design of active filters is considerably simpler than that of
passive ones. In addition, it's easy to provide for variability, which
can be used to change filter characteristics by electrical input signals.

The active filter also has some disadvantages:

1. Since the active filter contains electronic components, it requires
a power supply, which adds to the complexity of the realization. The
electronic components also place restrictions on the level of the signals
that can be applied to the filter and on the noise component that the
filter may add to the filtered signal.

2. The mathematical process by which the active filter produces filtering
characteristics in general requires the use of internal feedback. When
this feedback is positive, the resulting filter may be very sensitive
to lack of precision in component values, and the effects of aging and environmental conditions.

In general, active filters are designed with the assumption that the
active elements are ideal (no parasitics). For example, the operational
amplifier is assumed to have infinite gain, infinite input impedance,
zero output impedance, and an infinite frequency range (gain-bandwidth).
All practical filter realizations must be evaluated for the effect that
the nonideal parasitics have on actual filter performance. One of the
most trouble some of the parasitics is the operational-amplifier gain
band width. Typically, for a given application, tuning charts may be
developed which can be used to provide compensation for such operational-amplifier
limitations.